To find out how large the bacteria colony will be after 8 days given that it increases by 73% every 2 days, we need to follow these steps:
1. Initial Information:
- Initial number of bacteria (I): 150
- Growth rate (r): 73%
- Time period in days (t): 8 days
- Growth interval: every 2 days
2. Determine the Number of Intervals:
- The growth occurs every 2 days. Therefore, in 8 days, the number of intervals is:
[tex]\[
\text{Number of intervals} = \frac{8 \text{ days}}{2 \text{ days/interval}} = 4 \text{ intervals}
\][/tex]
3. Compound Growth Formula:
- The compound growth formula is given by:
[tex]\[
\text{Future Amount} = I \left(1 + r\right)^t
\][/tex]
4. Substitute the Known Values:
- Initial amount [tex]\(I = 150\)[/tex] bacteria
- Growth rate [tex]\(r = 0.73\)[/tex]
- Number of intervals [tex]\(t = 4\)[/tex]
Now substitute these values into the compound growth formula:
[tex]\[
\text{Future Amount} = 150 \left(1 + 0.73 \right)^4
\][/tex]
[tex]\[
\text{Future Amount} = 150 \left(1.73\right)^4
\][/tex]
5. Calculate the Future Amount:
- We compute the value of [tex]\(1.73^4\)[/tex]:
[tex]\[
1.73^4 \approx 8.95745
\][/tex]
- Now, multiply this by the initial amount:
[tex]\[
\text{Future Amount} = 150 \times 8.95745 \approx 1343.6175615
\][/tex]
Therefore, the size of the bacteria colony after 8 days will be approximately 1343.6175615 microorganisms.
